Results 31 to 40 of about 5,421,281 (277)
Bifurcations and Turing patterns in a diffusive Gierer–Meinhardt model
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer–Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both ...
Yong Wang, Mengping Guo, Weihua Jiang
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Hyperbolic Chaos of Turing Patterns [PDF]
Physical Review Letters, 2012 We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession.
Kuptsov, Pavel V. +2 more
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Mathematical Biosciences and Engineering, 2022 In this paper, we study the general mechanism of Turing-pattern in a tree-grass competition model with cross diffusion and time delay. The properties of four equilibrium points, the existence of Hopf bifurcation and the sufficient conditions for Turing ...
Rina Su, Chunrui Zhang
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Turing pattern with proportion preservation [PDF]
Journal of Theoretical Biology, 2006 Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the proportionality of the pattern, i.e., the ratio of the wavelength to the size, that is often required in biological ...
Ishihara, Shuji, Kaneko, Kunihiko
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Turing patterns in multiplex networks [PDF]
Physical Review E, 2014 The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled.
ASLLANI, MALBOR +4 more
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Allee effect-driven complexity in a spatiotemporal predator-prey system with fear factor
Mathematical Biosciences and Engineering, 2023 In this paper, we propose a spatiotemporal prey-predator model with fear and Allee effects. We first establish the global existence of solution in time and provide some sufficient conditions for the existence of non-negative spatially homogeneous ...
Yuhong Huo +4 more
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Physical Review Letters, 1993 Turing patterns involve regions of different chemical compositions which lead to density gradients that, in liquids, are potentially unstable hydrodynamically. Nonlinear hydrodynamics coupled with a model of Turing pattern formation show that convection modifies and coexists with some Turing patterns and excludes others, and thereby plays a significant
Vasquez, D. A. +2 more
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Turing patterns in three dimensions [PDF]
Physical Review E, 2007 We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium
Shoji, H, Yamada, K, Ueyama, D, Ohta, T
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Turing patterns in simplicial complexes
Physical Review E, 2023 The spontaneous emergence of patterns in nature, such as stripes and spots, can be mathematically explained by reaction-diffusion systems. These patterns are often referred as Turing patterns to honor the seminal work of Alan Turing in the early 1950s.
Shupeng Gao +3 more
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PLoS ONE, 2007 Les gradients de concentration à l'intérieur des cellules sont impliqués dans des processus clés tels que la division cellulaire et la morphogenèse. Nous montrons ici qu'un modèle de l'étape enzymatique catalysée par la phosphofructokinase (PFK), étape responsable de l'apparition d'oscillations homogènes dans la voie glycolytique, présente des motifs ...
Damián E. Strier, Silvina Ponce Dawson
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